Abstract In view of practical engineering and service deployment requirements, we propose to apply Lightpath Affiliation Graph partitioning heuristic for the wavelength assignment in mesh optical transport networks to support emerging lambda leasing service

Andrew K C Woo

C Y Li

P K A Wai

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Lightpath Affiliation Graph Approach for                           
Wavelength Assignment of Lambda Leasing Service                  
Andrew K. C. Woo, C. Y. Li, and P. K. A. Wai 
Department of Electronic and Information Engineering, The Hong Kong Polytechnic University,  
Hung Hom, Kowloon, Hong Kong SAR, China 
Phone: +(852) 63810107, Email: 01455121g@polyu.edu.hk
Abstract
In view of practical engineering and service deployment 
requirements, we propose to apply Lightpath Affiliation 
Graph partitioning heuristic for the wavelength 
assignment in mesh optical transport networks to support 
emerging lambda leasing service. 
Introduction 
Point-to-point or ring structure SONET/SDH 
technologies have been widely adopted by traditional 
network operators since its introduction in 90’s last 
century to support a variety of transport services. It is 
known that ring based networks suffer from poor 
scalability problem, i.e., six to eight nodes per ring are 
deployed for metro transport in practice. On the other 
hand, enterprise customers are demanding more 
bandwidth to support applications such as inter-sites 
backup, and fixed/mobile carriers are looking for low 
cost interconnection services. Owing to the need of using 
optical-electrical-optical (OEO) signal conversion, 
SONET/SDH technologies are not cost effective when it 
is used to support emerging high data rate applications. 
Therefore, the lambda leasing service (wave service)  [1] 
that offers end-to-end transparent wavelength channels 
(lightpaths) to connect customer sites directly is 
becoming important to network operators. Network 
operators are interested in mesh optical transport 
networks that can support transparent transmission 
services, promote architectural flexibility and save cost. 
Recently, the availability of reconfigurable optical add-
drop multiplexer (ROADM) has brought in multi-degree 
(steering optical signals to three or more trunk fiber 
ports) optical switching capability to enable mesh 
topology optical networks [2]. To deliver lambda leasing 
service successfully, however, an efficient and handy 
desktop planning tool that can address engineering and 
service deployment requirements to facilitate complex 
wavelength assignment in mesh optical networks should 
be available for network planners.  
The Lightpath Affiliation Graph Approach
Based on the experience of carrier class service 
deployment, a number of prevailing issues/criteria 
should be considered when we design the wavelength 
assignment tool. These issues/criteria include: 
1. The data communication equipment (e.g. switches, 
routers, media converters) at the customer ends 
normally equips with Small Form-factor Pluggable 
(SFP) transceiver of only a few specific wavelengths 
to minimize SFP stock variety; 
2. In general, edge ROADM does not come with the 
costly wavelength conversion capability. Therefore, 
two customer sites can interwork only if both SFPs 
operate on same wavelength channel; 
3. ROADM internal elements such as the ingress port 
filter for conditioning the SFP output signals to 
precise wavelength grid should be minimized; 
4. Higher tier customers require timely network 
management actions. The signal quality of these 
customers should be closely monitored; 
5. The number of customer access links should be 
minimized in a multi-fiber network (MFN); 
6. Commercial service is normally offered as cohort of 
readily available lightpaths. 
For Criterion 2, wavelength assignment should comply 
with the wavelength continuity constraint (WCC) such 
that same wavelength channel should be assigned for all 
of the links in a lightpath. Also, we cannot assign the 
same wavelength to two lightpaths on the same link, i.e., 
wavelength exclusivity constraint (WEC). Apart from 
WCC and WEC, one can observe that we should assign 
the same set of wavelength channels, if possible, 
amongst the same customer or same tier of customers. It 
will reduce the equipment and operation costs when 
lambda leasing service is offered to customers. We 
define that a group of lightpaths are compatible if they 
can be assigned to the same wavelength. An affiliated 
customer group is the group of customers having 
lightpaths of same set of wavelengths. An affiliated 
lightpath group is the largest group of compatible 
lightpaths assigned to the customers in an affiliated 
customer group. Hence, the wavelength assignment 
problem of lambda leasing service can then be turned 
into the problem of searching the appropriate affiliated 
lightpath groups. 
From an affiliated ligthpath group, we observe that 
the wavelength assignment problem is equivalent to the 
clique partitioning problem if we treat lightpaths as 
clique members. Clique is an affiliated group of 
compatible entities. The clique concept has been widely 
studied in research areas such as human behavior and 
graph theory. Although the general clique partitioning is 
also an NP-completed problem, a large number of 
mathematical tools are available to solve clique 
partitioning problems. Owing to the lightpath grouping 
nature of lambda leasing service, clique partitioning is 
ThH6
978-1-4244-4103-7/09/$25.0 © 2009 IEEE
more appropriate for network planning than general 
wavelength assignment methods [3,4].   
Using the eight-lightpath mesh network shown in 
Fig. 1(a) as an example, we demonstrate how clique 
partitioning can be used to solve the wavelength 
assignment problem of lambda leasing service. 
According to the WCC and WEC, we first draw a 
compatible graph for the ligthpaths in Fig. 1(b). Each 
lightpath i is denoted by a vertex vi. The compatibility 
relationship is denoted by an edge eij. There will be no 
edge eij if lightpaths i and j (vi and vj in Fig. 1(b)) share a 
common fiber link. This graph is called the basic 
Lightpath Affiliation Graph LAG (V,E) in lambda 
leasing service application. For customer B, a maximum 
complete sub-graph such as (v2-v3-v4) in Fig. 1(b) is a 
maximum clique representing one of possible affiliated 
lightpath group. In principle, we should select and 
partition the cliques based on affiliated customer groups. 
For demonstration purpose, however, we use a linear 
time iteration method [5] for clique partitioning and treat 
customers A and B as the same affiliated customer group. 
We select and delete the maximum clique in LAG at 
each round of iteration until the LAG becomes empty. 
For each maximum clique extraction, a wavelength is 
assigned to the associated lightpaths of maximum clique. 
The number of iterations will therefore equal to the 
number of wavelengths required. 
The proposed LAG heuristic has been verified with 
integer linear programming (ILP) wavelength 
assignment method using the random topology networks 
generated by Georgia Tech GT-ITM topology generator. 
Nine network topologies are shown in Table 1. Floyd-
Warshall shortest path algorithm is used to locate 
physical paths between every pair of source s and 
destination d. Traffic equations satisfying all flow 
constraints are modeled as ILP equations to yield 
minimal number of wavelengths as objective. An Intel 
x86 3GHz computer installed with CPLEX [6] was used 
to solve the ILP equations. Table 2 shows the required 
numbers of variables, constraints, memory and execution 
time for the ILP methods. From Table 2, we observe that 
ILP method can only solve the wavelength assignment 
problem of small networks, i.e., the required memory 
and execution time of ILP method grows exponentially 
with the network size. In Table 2, we also show the 
required execution time and minimum number of 
wavelengths when LAG heuristic is used for the 
wavelength assignment. The execution time of LAG 
heuristic is smaller than one second for all networks, i.e., 
the execution time of LAG heuristic will not be an 
important issue even for large networks. The required 
number of wavelengths solved by LAG heuristic is, in 
general, greater than that of ILP method because the ILP 
results are optimal. Owing to the simple iteration clique 
partitioning method, some LAG results such as network 
topologies 1, 2 and 4 require 33 to 44 % more 
wavelengths than that of ILP method. It is expected that 
we can have much better wavelength assignment result if 
sophisticated clique partitioning methods is used.  
The major advantage of clique partitioning for 
wavelength assignment is its intuitive relation with the 
affiliated lightpath group. Besides, LAG ensures that 
dedicated wavelength is assigned to affiliated customer 
groups. For example, we can simply apply a graph “cut” 
as shown in Fig. 1(b) to the basic LAG to have distinct 
wavelengths assigned to customer A and B. Edges eij will 
be removed from the basic LAG (V,E) if lightpaths i and 
j (vi and vj in Fig. 1(b)) belong to different affiliated 
customer groups. Such arrangement allows flexibility to 
further tighten the affiliation criteria to suit practical 
provisioning considerations. Recently, a wavelength 
assignment method also proposed to apply clique 
partitioning to solve wavelength assignment in mesh 
networks [4]. However, the method has not been aware 
of the relationship between maximum clique and 
affiliated ligthpath group. If the clique partitioning 
approach is only used to solve general wavelength 
assignment problems, we envisage that no special 
advantage can be obtained as compared to the 
sophisticated wavelength assignment heuristics [3]. 
References  
1. J. Berthold et al., Journal of Lightwave Technology (May 
2008), p1104-1118 
2. P. Morkel, Lightwave Europe (Q1, 2008), p15-18 
3. Z. Hui, Optical Network Magazine (Jan. 2000), p47-60 
4. S.Rao et al., ICDCN (2008), p452-463 
5. E. Balas and C. S. Yu, SIAM J. Computing (Nov. 1986), 
vol. 15, p1054-1068 
6. ILOG, CPLEX Optimizer 11.0.0, www.ilog.com
1
2
3
6
7
8
7
6 5
4
3
21
8
Cut
5
4
1
8
7 6
3
xNode Lightpath index
Link Lightpath
x Denote the lightpath index
Denote compatible lightpaths
Fig. 1. (a) Eight-lightpaths network        (b) LAG with graph “cut”
4
5
2
Lightpaths index of customer A: 5,6,7,8
Lightpaths index of customer B: 1,2,3,4
Topology 
Model Variable Constraint Mps file size
Read 
time (s)
Sol. 
Time (s) ILP obj.
Sol. 
Time (s)
LAG 
obj.
1. RWA_10-0 31321 10174 7,075,694 1.24 39.77 12 1 16
2. RWA_10-1 33481 10200 7,553,370 1.34 1.51 9 1 12
3. RWA_10-2 51751 20912 11,747,674 2.11 3.75 21 1 21
4. RWA_15-0 233101 89526 53,630,022 1.64 1550 25 1 36
5. RWA_15-1 321301 89960 73,319,650 9.72 7809 26 1 26
6. RWA_15-2 378841 131370 86,900,870 14.39 14086 44 1 44
7. RWA_20-0 1079201 292050 247,779,430 1 27
8. RWA_20-1 1048801 291968 240,958,666 1 39
9. RWA_20-2 1079201 292050 240,958,666 1 28
Integer Linear Programming (CPLEX) LAG approach
Table 2. Comparison between ILP and LAG methods 
Model Size (node, edges) Model Size (nodes, edges) 
1.RWA_10-0 10 nodes, 14 edges 6.RWA_15-2 15 nodes, 20 edges 
2.RWA_10-1 10 nodes, 15 edges 7.RWA_20-0 20 nodes, 35 edges 
3.RWA_10-2 10 nodes, 11 edges 8.RWA_20-1 20 nodes, 34 edges 
4.RWA_15-0 15 nodes, 18 edges 9.RWA_20-2 20 nodes, 35 edges 
5.RWA_15-1 15 nodes, 25 edges 
Table 1. Network models generated by GT-ITM 


Lightpath Affiliation Graph Approach for Wavelength Assignment of Lambda Leasing Service

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Lightpath Affiliation Graph Approach for Wavelength Assignment of Lambda Leasing Service

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